The British 1797 Penny does not have stars on it.
Due to Britains ongoing expenses with various wars in the late 18th and early 19th centuries, there were very few silver or copper coins minted, subsequently there were a great many privately minted tokens and counterfeit coins produced.
To get an estimate of value on a privately minted token, you need to provide the details of the inscription on the token.
The British "Cartwheel Penny" and "Cartwheel TwoPence" were only issued in 1797. The Isle of Man "Cartwheel Penny" and "Cartwheel Halfpenny" were issued in 1798 and 1813. Any of these coins in excellent condition could be considered valuable.
More information is needed - is it a British penny or American cent? Please post a new, separate question with the name of the country that issued the coin.
The British 1797 "Cartwheel" Proof Penny was minted in a variety of metals including, Gilt copper, Copper, Bronzed, Silver and Gold. Mintage figures are not given since coins from this period were usually produced by a specific weight, ie. two tonnes of Pennies. Most of the 1797 Proof coins are rated as various degrees of "rare".
Your coin is either a British 1797 "Cartwheel" Twopence 41mm in diameter, or a British 1797 "Cartwheel" Penny 36mm in diameter. If somebody has drilled a hole in it, it might be worth a few Pence. Modified coins have no collector value.
There were no British Halfcrown coins minted from 1752 to 1815 inclusive.
The only British copper coins minted in 1797 were the Cartwheel Penny and the Cartwheel Twopence. They were referred to as "Cartwheel" coins because of the distinctive rim around the edge of the coins giving the appearance of a cartwheel. Exact mintage figures can only be guessed at since the mintage for 1797 was referred to in tons of coins. There was a combined mintage of 5 tons of British Penny and Twopence coins minted in 1797. These were the first British copper coins to have been minted in over 20 years. The 1797 Penny weighed 1 ounce or 28.35 grams. The 1797 Twopence weighed 2 ounces or 56.7 grams.
Apart from George III, the only person depicted on British 1797 coins is Britannia, the female personification of Britain. She is usually shown as being seated and holding a trident and shield. In 1797 she is on the reverse of the "Cartwheel" Twopence and the "Cartwheel" Penny.
If you refer to the British 1797 Penny and Twopence coins, they may have been cursed by the people who had to use them. Both coins were very big and very heavy, even by the standards of the day. The 1797 "Cartwheel" Penny weighed 1 ounce or 28.35 grams and was 36 mm in diameter. The 1797 "Cartwheel" Twopence weighed 2 ounces or 56.7 grams and was 41 mm in diameter.
If you refer to the GEORGE III 1797 "Cartwheel" Penny and Twopence, they are both made from copper and are of almost identical appearance, the Penny is a little over 30 mm in diameter and the Twopence is much larger at about 40 mm in diameter.
You have described every British coin issued in 1797. Please provide the type of metal it appears to be made from, the diameter of the coin, the inscriptions and the design on the reverse.
There were no British Threepences minted in 1797, bronze or otherwise. Other than Maundy coins, the only Threepences known to have been minted between 1786 and 1833 were the 1792, 1795 and 1800 coins.
The obverse of any King George coin will have King George on it. From 1714 to 1952 there were 6 King Georges. From 1714 to 1800, the reverse of the British silver Penny had a Crowned "1" on it. From 1797 to 1967, the reverse of the British copper and bronze Penny featured the seated figure of Britannia holding a trident and shield.